An ellipsis

Aug 2018
128
7
România
Good evening to all,

Let \(\displaystyle M\) be a point outside the ellipse \(\displaystyle ϵ (a, b, O)\), and \(\displaystyle MT_1\) and \(\displaystyle MT_2\) are the two tangent lines to the ellipse. Line \(\displaystyle MO\) intersects the ellipse at points \(\displaystyle N\) and \(\displaystyle P\). Calculate:

1)\(\displaystyle | MT_1^2 - MT_2^2 |\)

2) \(\displaystyle | MN⋅MP - MT_1^2 |\)

3) \(\displaystyle | MN⋅MP - MT_2^2 |\)

All the best,

integrator
 
Last edited:

v8archie

Math Team
Dec 2013
7,709
2,677
Colombia
And the ellipsis…?